Related papers: On unitary deformations of smooth modular represen…

For a locally compact group $G$, we show that it is possible to present the class of continuous unitary representations of $G$ as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how…

In this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of normed modules, thus providing a notion of precise…

Let $F$ be locally compact field with residue characteristic $p$, and $\mathbf{G}$ a connected reductive $F$-group. Let $\mathcal{U}$ be a pro-$p$ Iwahori subgroup of $G = \mathbf{G}(F)$. Fix a commutative ring $R$. If $\pi$ is a smooth…

In this article we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As…

Let $\pi_1$ and $\pi_2$ be absolutely irreducible smooth representations of $G=GL_2(Q_p)$ with a central character, defined over a finite field of characteristic $p$. We show that if there exists a non-split extension between $\pi_1$ and…

The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…

We construct a representation of the affine W-algebra of gl_r on the equivariant homology space of the moduli space of U_r-instantons on A^2, and identify the corresponding module. As a corollary we give a proof of a version of the AGT…

We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique…

In this paper, we study the representation theory of the universal central extension $\mathcal{G}$ of the infinite-dimensional Galilean conformal algebra, introduced by Bagchi-Gopakumar, in $(2+1)$ dimensional space-time, which was named…

The known duality of the space of Bloch complex-valued functions on the open complex unit disc $\mathbb{D}$ is addressed under a new approach with the introduction of the concepts of Bloch molecules and Bloch-free Banach space of…

In this article, we study admissible representations of even unitary groups over local fields, where the quadratic extension is ramified, with invariant vectors under the action of the stabilizer of a unimodular lattice and some properties…

In this paper we study random representations of fundamental groups of surfaces into special unitary groups. The random model we use is based on a symplectic form on moduli space due to Atiyah, Bott, and Goldman. Let $\Sigma_{g}$ denote a…

The purpose of the current paper is to introduce some new methods for studying the $p$-adic Banach spaces introduced by Emerton \cite{emerton}. We first relate these spaces to more familiar sheaf cohomology groups. As an application, we…

It was suggested on several occasions by Deligne, Drinfeld and Kontsevich that all the moduli spaces arising in the classical problems of deformation theory should be extended to natural "derived" moduli spaces which are always smooth in an…

In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining…

In this note, we address a question raised by Kr\"otz on the classification of domains of holomorphy of irreducible admissible Banach representations for connected non-compact simple real Lie groups G. When G is not of Hermitian type, we…

This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a…

An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=\alpha$ in some…

These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields of positive characteristic, obtained in joint work with G.…

We will define and study (moduli) spaces of deformations of irregular classes on Riemann surfaces, which provide an intrinsic viewpoint on the `times' of irregular isomonodromy systems in general. Our aim is to study the deeper…